Question: Simplify the following expression: $ k = \dfrac{1}{7} + \dfrac{2r}{5r - 5} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5r - 5}{5r - 5}$ $ \dfrac{1}{7} \times \dfrac{5r - 5}{5r - 5} = \dfrac{5r - 5}{35r - 35} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{2r}{5r - 5} \times \dfrac{7}{7} = \dfrac{14r}{35r - 35} $ Therefore $ k = \dfrac{5r - 5}{35r - 35} + \dfrac{14r}{35r - 35} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{5r - 5 + 14r}{35r - 35} $ $k = \dfrac{19r - 5}{35r - 35}$